Is there anything like alimony or child support in Sharia law?
Depends on which version of
shariah. I don't know a whole lot about
shariah under Sunni
madh'hab, but according to a number of
faqih in Shia Islam, there's no actual alimony as we understand it, but if a man divorces his wife, she can keep the
Mahr (a mutually-agreed-upon amount given by the husband to the wife as a marriage gift, similar to but not exactly like a Western dowry), and during the required waiting period after a divorce before remarriage is permitted (
'Iddah, which generally lasts three full menstrual cycles) the husband has to pay the wife's maintenance. It's also recommended that the husband pay an amount over and above the
Mahr and the
'Iddah maintenance to the wife, to make post-marriage life easier for her (in accordance with Qur'an 2:231's admonition "When you divorce women, and they have reached their waiting-period, then either retain them in a fair manner or set them free in a fair manner").
As for child support, according to Sayyid Moustafa al-Qazwini (also a Shia
faqih), if parents can't agree on a custody arrangement, the child stays with the father. If the father isn't suitable or capable to raise the child, or if the parents agree, the child stays with the mother, but in that case the father is obligated to financially support his children.
In Shia Islam, the repetition of the
talaq, or divorce pronouncement, has to be done on separate occasions (as Shahid Ayatollah Murtadha Mutahhari put it, "the three words, ‘I divorce you’ can be repeated 100 times in one go and still be considered one divorce" out of the required three divorces), as well as before two witnesses, so an email or text containing those words repeated three times won't result in a valid divorce under Shia
shariah.
As a side note, while women can't divorce their husbands using the above method, there are ways under
shariah that a woman can initiate a divorce. And, as Grand Ayatollah al-Sistani has ruled, if a Muslim woman living in the West obtains a divorce order in a secular Western court, she
has to be granted a
shariah divorce regardless of whether the husband wants a divorce or not.
EDIT:
I believe that a Muslim woman could write into her marriage contract that she could divorce her husband the same way, if they both agreed to it.
This is true. According to Maqbul Hussein Rahim, "[t]he bride may, in the
mahr, confer upon herself a right to divorce, or provide for the division of property in the event of divorce or any other condition to reserve for herself any right or benefit which under the
shariah she would not normally enjoy." (While normally a monetary amount, the
mahr can also be a promise exacted from the husband-to-be to fulfill a condition or obligation imposed by the bride-to-be. That's part of why it's not exactly like a Western dowry.)